The present invention relates to a triangular-pyramidal cube-corner retroreflective sheeting having a novel structure. More minutely, the present invention relates to a triangular-pyramidal cube-corner retroreflective sheeting characterized in that triangular-pyramidal reflective elements respectively having a novel structure are arranged in the closest-packed state.
Still more minutely, the present invention relates to a triangular-pyramidal cube-corner retroreflective sheeting constituted of triangular cube-corner retroreflective elements (hereafter also referred to as triangular-pyramidal reflective elements or merely referred to as elements) useful for signs including license plates of automobiles and motorcycles, safety materials of clothing and life jackets, markings of signboards, and reflectors of visible light, laser beams, and infrared-ray reflective sensors.
Still more minutely, the present invention relates to a triangular-pyramidal cube-corner retroreflective sheeting characterized in that triangular-pyramidal cube-corner retroreflective elements protruded beyond a first common bottom plane (virtual plane X-Xxe2x80x2) are arranged so as to be faced each other in the closest-packed state on the first bottom plane (virtual plane X-Xxe2x80x2) by sharing each base edge on the first bottom plane (virtual plane X-Xxe2x80x2), the first bottom plane (virtual plane X-Xxe2x80x2) is a common plane including the base edges (x, x, . . . ) shared by the triangular-pyramidal reflective elements, two opposite triangular-pyramidal reflective elements form a substantially-same-shape element pair faced each other so as to be substantially symmetric to planes (Y-Yxe2x80x2, Y-Yxe2x80x2, . . . ) vertical to the first bottom plane including the shared base edges (x, x, . . . ) on the first bottom plane (virtual plane X-Xxe2x80x2), the triangular-pyramidal reflective elements are formed by substantially same triangular lateral faces (faces c1 and c2) using each of the shared base edges (x, x, . . . ) as one side and two substantially same quadrangular lateral faces (faces a1 and b1 or faces a2 or b2) substantially perpendicularly crossing the lateral faces (faces c1 and c2), which (the above lateral faces a1 and b1 or lateral faces a2 or b2) use each of two upper sides of the triangular lateral faces (faces c1 and c2) started from apexes (H1 and H2) of the triangular-pyramidal reflective elements as one side and share one ridge line of the triangular-pyramidal reflective elements as one side, and the height (hxe2x80x2) from the apexes (H1 and H2) of the triangular-pyramidal reflective elements up to the first bottom plane (virtual plane X-Xxe2x80x2) including the base edges (x, x, . . . ) of the triangular lateral faces (faces c1 and c2) of the triangular-pyramidal reflective elements is substantially smaller than the height (h) from the apexes (H1 and H2) of the triangular-pyramidal reflective elements up to a substantilly-horizontal second bottom plane (Z-Zxe2x80x2) including base edges (z and w) of other lateral faces (faces a1 and b1 or faces a2 or b2) of the triangular-pyramidal reflective elements.
A retroreflective sheeting is well known which reflects incoming light toward a light source and the sheeting using its retroreflective performance is widely used for the above application fields. Particularly, a retroreflective sheeting using the retroreflection principle of a cube-corner retroreflective element such as a triangular-pyramidal reflective element is exceptionally superior to a conventional retroreflective sheeting using micro-glass-beads in retroreflective efficiency of light and its purpose has expanded year by year because of its superior retroreflective performance.
However, though a conventionally publicly-known triangular-pyramidal retroreflective element shows a preferable retroreflective efficiency in a range of a small angle formed between the optical axis of the element (axis passing through the apex of a triangular pyramid which is present at the equal distance from three faces crossing each other at 90xc2x0 and which constitutes a triangular-pyramidal cube-corner retroreflective element) and an entrance ray (this small angle is hereafter referred to as entrance angle), the retroreflective efficiency is suddenly deteriorated as the entrance angle increases (that is, entrance angularity is deteriorated).
Moreover, the reflection principle of a triangular-pyramidal retroreflective element conforms to the internal total reflection caused at the interface between air and a transparent medium constituting the triangular-pyramidal reflective element when light is transmitted into the air from the transparent medium at a specified angle {critical angle (xcex1c)} or more. The critical angle (xcex1c) is shown by the following expression in accordance with the refractive index (n) of the transparent medium and the refractive index (nxe2x80x2) of the air.       sin    ⁢          xe2x80x83        ⁢          α      c        =            n      xe2x80x2        n  
In the above expression, because it is assumed that the refractive index (nxe2x80x2) of the air is almost equal to 1 and constant, the critical angle (xcex1c) decreases as the value of the refractive index (n) of the transparent medium increases and thereby, light more easily reflects at the interface between the transparent medium and the air. In general, because most synthetic resins have a refractive index of approx. 1.5, the critical angle (xcex1c) becomes a comparatively large value of approx. 42xc2x0.
Light incoming to the surface of a retroreflective sheeting using the above triangular-pyramidal reflective element at a large entrance angle passes through the triangular-pyramidal reflective element and reaches the interface between the element and air at a comparatively small angle. When the angle is less than the critical angle (xcex1c), the light is transmitted to the back of the element without totally reflecting from the interface. Therefore, a retroreflective sheeting using a triangular-pyramidal reflective element generally has a disadvantage that the entrance angularity is inferior.
However, because a triangular-pyramidal retroreflective element can reflect light in the direction from which the light enters almost over the entire surface of the element, reflected light does not diverge in a wide angle due to spherical aberration like the case of a micro-glass-bead reflective element.
However, the narrow divergent angle of the retroreflected light easily practically causes a trouble that when the light emitted from the head lamp of an automobile retroreflects from a traffic sign, the retroreflected light doe not easily reach eyes of a driver present at a position separate from the optical axis of the light. The trouble of this type more frequently occurs (that is, an observation angle is deteriorated) because the angle (observation angle) formed between the entrance axis of rays and the axis (observation axis) connecting a driver with a reflection point increases particularly when an automobile approaches a traffic sign.
For the above cube-corner reflective sheeting, particularly a triangular-pyramnidal cube-corner retroreflective sheeting, many proposals have been known and various improvements and studies have been made.
For example, Jungersen""s U.S. Pat. No. 2,481,757 discloses a retroreflective sheeting constituted by arranging retroreflective elements of various shapes on a thin sheet and a method for manufacturing the sheeting. The above U.S. patent discloses a triangular-pyramidal reflective element whose apex is located at the center of a bottom-plane triangle and a tilted triangular-pyramidal reflective element whose apex is not located at the center of a bottom-plane triangle and that light is efficiently reflected toward an automobile coming nearer. Moreover, it is disclosed that a triangular-pyramidal reflective element has a depth of {fraction (1/10)} in (2,540 xcexcm) or less. Moreover, FIG. 15 of the above U.S. patent illustrates a triangular-pyramidal reflective element pair whose optical axis is tilted in the positive (+) direction which is opposite to the case of a preferred embodiment of the present invention whose optical axis is tilted in the negative (xe2x88x92) direction. The tilt angle (xcex8) of the optical axis is estimated as approx. 6.5xc2x0 when calculating the angle in accordance with the ratio between the major and minor sides of the bottom-plane triangle of the illustrated triangular-pyramidal reflective element.
However, the above Jungersen""s U.S. patent does not specifically discloses a very-small triangular-pyramidal reflective element disclosed by the present invention or does not disclose or suggest a size and an optical-axis tilt of a triangular-pyramidal reflective element required to obtain superior observation angularity and entrance angularity.
In this specification, as described later in detail, the expression xe2x80x9ctilted in a direction in which optical axis becomes negative (xe2x88x92)xe2x80x9d denotes that when triangular-pyramidal reflective elements protruded beyond a common plane (X-Xxe2x80x2) share each of base edges (x, x, . . . ) and bottom planes of the reflective elements are arranged in the closest-packed state on the common plane (X-Xxe2x80x2) including the base edges (x, x, . . . ) shared by the retroreflective elements as element pairs faced so as to be substantially symmetric to a plane (Y-Yxe2x80x2) vertical to the common plane (X-Xxe2x80x2), the optical axis tilts in a direction in which the difference (qxe2x88x92p) between the distance (q) from the intersection (Q) between the optical axis of the triangular-pyramidal reflective elements and the common plane (X-Xxe2x80x2) up to the plane (Y-Yxe2x80x2) vertical to the plane (X-Xxe2x80x2) and the distance (p) from the intersection (P) between a vertical line extended from the apexes (H1 and H2) of the elements to the bottom plane of the elements and the plane (X-Xxe2x80x2) up to the vertical plane (Y-Yxe2x80x2) becomes negative (xe2x88x92). Moreover, the state in which the optical axis tilts in a direction in which (qxe2x88x92p) becomes positive (+) is hereafter shown asxe2x80x9ctilted in a direction in which optical axis becomes positive (+)xe2x80x9d.
Furthermore, Stamm""s U.S. Pat. No. 3,712,706 discloses a retroreflective sheeting in which so-called equilateral-triangular-pyramidal cube-corner retroreflective elements whose bottom-plane shapes are equilateral triangles are arranged on a thin sheeting so that bottom planes of the elements are brought into the closest-packed state. The above Stamm""s U.S. patent improves the problem of deterioration of a retroreflective efficiency due to increase of an entrance angle and the above trouble that light incoming at an angle less than the internal total reflection condition passes through the interface between elements and thereby, it does not retroreflect by applying vacuum evaporation to the reflection face of a reflective element to cause mirror reflection.
However, because the above Stamm""s proposal uses the mirror-reflection principle as means for improving wide angularity, a trouble easily occurs that the appearance of an obtained retroreflective sheeting becomes dark or reflectivity easily deteriorates because a metal such as aluminum or silver used for a mirror-face layer is oxidized by water or air in service. Moreover, means for improving wide angularity in accordance with a tilt of an optical axis is not described at all.
Moreover, Hoopman""s European Pat. No. 137,736(B1) discloses a retroreflective sheeting in which tilted triangular-pyramidal cube-corner retroreflective elements with isosceles bottom-plane triangles are arranged on a thin sheeting so that bottom planes of the elements are brought into the closest-packed state on the common plane. The optical axis of the triangular-pyramidal cube-corner retroreflective element disclosed in the above patent tilts in a negative (xe2x88x92) direction similarly to the tilt direction of the optical axis of a preferred triangular-pyramidal reflective element of the present invention and its tilt angle ranges between 7xc2x0 and 13xc2x0.
However, according to the relation between reflectivity and optical-angle tilt by the light tracking method attempted by the present inventor et al., it is found that reflectivity deteriorates as the tilt angle of the optical axis increases exceeding 4xc2x0 in the negative direction, particularly the reflectivity of a triangular-pyramidal reflective element whose optical-axis tilt exceeds 6xc2x0 in the negative direction is extremely deteriorated. This may be because though areas of three prism faces a, b, and c forming a triangular-pyramidal reflective element whose optical axis is not tilted are equal to each other, areas of faces a and b of an element whose optical axis is tilted gradually decrease compared to the area of the face c of the element as the tilt angle of the optical axis increases.
Moreover, Szczech""s U.S. Pat. No. 5,138,488 discloses a retroreflective sheeting in which tilted triangular-pyramidal cube-corner retroreflective elements with isosceles bottom-plane triangles are arranged on a thin sheeting so that bottom planes of the elements are brought into the closest-packed state on the common plane. In the case of this U.S. patent, optical axes of the triangular-pyramidal reflective elements tilt in the direction of a side shared by two triangular-pyramidal reflective elements which are faced each other and paired and it is specified that the tilt angle ranges between about 2xc2x0-5xc2x0 and each element has a size of 25 to 100 xcexcm.
Moreover, in the case of European Patent No. 548,280(B1) corresponding to the above U.S. patent, it is disclosed that the distance between a plane including the common side of two paired elements and vertical to a common plane and the apex of the element is not equal to the distance between the intersection between the optical axis of the element and the common plane and the vertical plane, that is, the direction of the tilt of the optical axis is positive (+) or negative (xe2x88x92), and the tilt angle ranges between about 2xc2x0-5xc2x0, and the element has a size of 25 to 100 xcexcm.
As described above, in the case of Szczech""s European Pat. No. 548,280(B13), the tilt of an optical axis ranges between xc2x12xc2x0 and xc2x15xc2x0. However, it is impossible to obtain completely improvement of wide angularity, particularly improvement of entrance angularity from the tilt of the optical axis in the range of Szczech""s invention.
The triangular-pyramidal cube-corner retroreflective elements of the above-described already-publicly-known Jungersen""s U.S. Pat. No. 2,481,757, Stamm""s U.S. Pat. No. 3,712,706, Hoopman""s European Pat. No. 137,736(B1), Szczech""s U.S. Pat. No. 5,138,488, and European Pat. No. 548,280(B1) are common in that bottom planes of many triangular-pyramidal reflective elements serving as cores of entrance and reflection of light are present on the same plane and each of retroreflective sheetings constituted of the triangular-pyramidal reflective elements whose bottom planes are present on the same plane has a disadvantage that the sheeting is inferior in entrance angularity, that is, when the entrance angle of rays to each triangular-pyramidal reflective element increases, the retroreflectivity is suddenly deteriorated.
As basic optical characteristics requested for a triangular-pyramidal cube-corner retroreflective sheeting, high reflectivity, that is, not only intensity (magnitude) of reflectivity represented by the reflectivity of light incoming from the front of the sheeting but also wide angularity are requested. Moreover, observation angularity, entrance angularity, and rotation angularity are requested for the wide angularity.
As described above, retroreflective sheetings constituted of the already-publicly-known triangular-pyramidal cube-corner retroreflective elements are all inferior in entrance angularity and moreover, they are not satisfactory in observation angularity in general. However, the present inventor et al. find through light tracking simulations that it is possible to improve the entrance angularity of a retroreflective sheeting constituted of the triangular-pyramidal reflective element by making the height (hxe2x80x2) from apexes (H1 and H2) of the triangular-pyramidal reflective elements up to a first bottom plane (virtual plane X-Xxe2x80x2) including base edges (x, x, . . . ) of triangular lateral faces (faces c1 and c2) of the triangular-pyramidal ,reflective element smaller than the height (h) from the apexes (H1 and H2) of the triangular-pyramidal reflective element up to a substantially-horizontal second bottom plane (Z-Zxe2x80x2) including base edges (z and w) of other lateral faces (faces a1 and b1 or faces a2 or b2) of the triangular-pyramidal reflective element.
More minutely, the present invention relates to a triangular-pyramidal cube-corner retroreflective sheeting in which triangular-pyramidal cube-corner retroreflective elements protruded beyond a first common bottom plane (virtual plane X-Xxe2x80x2) are arranged so as to be faced each other in the closest-packed state on the first bottom plane (virtual plane X-Xxe2x80x2) by sharing each base edge on the first bottom plane (virtual plane X-Xxe2x80x2), the first bottom plane (virtual plane X-Xxe2x80x2) is a common plane including the base edges (x, x, . . . ) shared by the triangular-pyramidal reflective elements, two opposite triangular-pyramidal reflective elements form a substantially-same-shape element pair faced each other so as to be substantially symmetric to planes (Y-Yxe2x80x2, Y-Yxe2x80x2, . . . ) vertical to the first bottom plane including the shared base edges (x, x, . . . ) on the first bottom plane (virtual plane X-Xxe2x80x2), the triangular-pyramidal reflective elements are formed by substantially same triangular lateral faces (faces c1 and c2) using each of the shared base edges (x, x, . . . ) as one side and two substantially same quadrangular lateral faces (faces a1 and b1 or faces a2 or b2) substantially perpendicularly crossing the lateral faces (faces c1 and c2), which (the above lateral faces a1 and b1 or lateral faces a2 or b2) use each of two upper sides of the triangular lateral faces (faces c1 and c2) started from apexes (H1 and H2) of the triangular-pyramidal reflective elements as one side, and share one ridge line of the triangular-pyramidal reflective elements as one side, and the height (hxe2x80x2) from the apexes (H1 and H2) of the triangular-pyramidal reflective elements up to the first bottom plane (virtual plane X-Xxe2x80x2) including the base edges (x, x, . . . ) of the triangular lateral faces (faces c1 and c2) of the triangular-pyramidal reflective elements is substantially smaller than the height (h) from the apexes (H1 and H2) of the triangular-pyramidal reflective elements up to a substantially-horizontal second bottom plane (Z-Zxe2x80x2) including base edges (z and w) of other lateral faces (faces a1 and b1 or faces a2 or b2) of the triangular-pyramidal reflective elements.
A more-preferable triangular-pyramidal cube-corner retroreflective sheeting of the present invention is characterized in that triangular-pyramidal cube-corner retroreflective elements protruded beyond a first common bottom plane (virtual plane X-Xxe2x80x2) are faced each other and arranged on the first bottom plane in the closest-packed state by sharing each base edge on the first bottom plane (virtual plane X-Xxe2x80x2), the first bottom plane (virtual plane X-Xxe2x80x2) is a common plane including the base edges (x, x, . . . ) shared by the triangular-pyramidal reflective elements, two opposite triangular-pyramidal reflective elements form a substantially-same-shape element pair faced so as to be symmetric to planes (Y-Yxe2x80x2, Y-Yxe2x80x2, . . . ) vertical to the first bottom plane including shared base edges (x, x, . . . ) on the first bottom plane (virtual plane X-Xxe2x80x2), lateral faces (faces c1 and c2) using each of the shared base edges (x, x, . . . ) of the triangular-pyramidal reflective elements as one side form substantially same triangles and are arranged along the shared base edges (x, x, . . . ), two other lateral faces (faces a1 and b1 or faces a2 or b2) form substantially same quadrangular lateral faces by using each of two upper sides of the triangular lateral faces (faces c1 and c2) started from apexes (H1 and H2) of the triangular-pyramidal reflective elements as one side and sharing one ridge line of the triangular-pyramidal reflective elements as one side, a second bottom plane (Z-Zxe2x80x2) including base edges (z and w) of the lateral faces (faces a1 and b1) formed because the quadrangular lateral faces (faces c1 and c2) cross the corresponding quadrangular lateral faces (face a2 or face b2) of other adjacent triangular-pyramidal reflective elements is substantially parallel with the first bottom plane (virtual plane X-Xxe2x80x2), located substantially below the first bottom plane (virtual plane X-Xxe2x80x2) including base edges (x, x, . . . ) of the triangular-pyramidal reflective elements, and tilted in a direction in which the difference (qxe2x88x92p) between the distance (q) from the intersection (Q) between the optical axis via apexes of the triangular-pyramidal reflective elements and the second bottom plane (Z-Zxe2x80x2) up to a plane (Y-Yxe2x80x2) including base edges (x, x, . . . ) shared by the element pair and vertical to the first bottom plane (X-Xxe2x80x2) and the distance (p) from the intersection (P) between a vertical line extended from the apexes (H1 and H2) of the elements up to the second bottom plane (Z-Zxe2x80x2) up to the vertical plane (Y-Yxe2x80x2) including the base edges (x, x, . . . ) shared by the element pair becomes negative (xe2x88x92) so that the optical axis tilts by at least 3xc2x0 from the vertical line (H1-P) extended from apexes of the triangular-pyramidal reflective elements to the second bottom plane.